Cluster 1: Develop understanding of fractions as numbers. (Major Cluster)Archived

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

In this interactive Flash game, students are challenged to identify a fraction from a picture of a group of objects or from a geometric diagram, or they are asked to create a diagram or picture given a common fraction. Motivation is provided by earning buckets of sand to built a sand castle.

Type: Educational Game

This interactive, online game is a fun way for students to practice identifying fractions. In this lesson students identify fractions to help a man hop his way across a river.

Type: Educational Software / Tool

Students are shown three circles and asked to select the one that correctly shows one third shaded and explain why the other two do not.

Type: Formative Assessment

Students are shown the fraction one fifth and asked to describe what it means.

Type: Formative Assessment

Students are read a word problem about a student who has run three-fourths of a race and asked to describe what that means.

Type: Formative Assessment

Students are read a word problem about a wall being painted and asked to describe what three-eighths of the wall means.

Type: Formative Assessment

Students are given a number line scaled by fourths and ask to label the notches.

Type: Formative Assessment

Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.

Type: Formative Assessment

Students are asked to divide two rectangles into fourths and then to consider how many fourths the two wholes represent.

Type: Formative Assessment

Students compare two pairs of fractions and record their comparisons using the less than or greater than symbols.

Type: Formative Assessment

Students compare two fractional parts of two different wholes.

Type: Formative Assessment

Students determine whether or not fractions are equivalent.

Type: Formative Assessment

Students are asked to use a number line that includes the location of zero and one-sixth to find the location of four-sixths.

Type: Formative Assessment

Students are given four number line diagrams and asked to choose the one that correctly shows the location of one-third.

Type: Formative Assessment

Students are asked to locate five-eighths on a number line that has been anchored by zero and one, but that has not yet been scaled.

Type: Formative Assessment

Students are asked to scale a number line from zero to one so that they can find the location of three-fourths.

Type: Formative Assessment

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

Students will represent fractions between zero and one by completing a number line of their own. Students will use their understanding of fractions between zero and one to design their own number line. Students will then communicate their understanding of representing fractions on a number line through a written proposal.

Type: Lesson Plan

This problem-solving lesson has students working together in groups to discover that fractions are made up of equal parts of one-whole. In this lesson, students are exposed to equivalent fractions as well as challenged to work beyond unit fractions to discover the fractional part of one-whole that the "mystery strips" represent. This highly engaging lesson takes into account all levels of learners and will challenge even your most advanced students.

Type: Lesson Plan

In this lesson, students will recognize a whole partitioned into equal parts and represent the unit fraction as 1/b. Students will learn to represent one equal-sized piece (numerator) of the partitioned whole (denominator) as a number in standard, numeral-word, and word form.

Type: Lesson Plan

This lesson will help students understand that fractions are parts of a whole. The lesson introduces fractional parts using familiar manipulatives.

Type: Lesson Plan

The students will receive paper pizzas that are divided into different fractional parts. They will decorate their pizza, and then make equal trades with classmates to explore equivalence of fractions.

Type: Lesson Plan

In this lesson students will make initial discoveries about fractions. Students will work together to explain and record the discoveries they make while using manipulatives to explore fractions.

Type: Lesson Plan

In this lesson, students will create a human number line by estimating a fraction's approximate location on the number line between zero and one. This lesson helps students visualize fractions’ relative distance from 0 in order to order and compare fractions and engages them in justifying their thinking.

Type: Lesson Plan

This lesson is designed to introduce and give students practice with the concept of fractions as part of a set. Students will use their classmates to create fraction statements, play a guessing game with color tiles, and finally write fractional statements about their own Name Art!

Type: Lesson Plan

This lesson is designed to help students generate rules for comparing fractions. The students will use fraction tiles to discover ways to compare fractions with the same denominator or fractions with the same numerator. They will also begin to use benchmark fractions to help make comparisons and complete inequalities.

Type: Lesson Plan

In this lesson, students will extend their understanding of unit and non-unit fractions by using different pattern blocks to represent one whole and then determining the fractional part the other pattern blocks represent.

Type: Lesson Plan

Would you rather have 2/4 or 6/12 of a Hershey Chocolate Bar? The students will create a fraction tool kit from construction paper to investigate equivalent fractions using rectangular area models.

Type: Lesson Plan

This lesson provides a conceptual approach to multiplying a fraction times a whole number and a whole number times a fraction.  Students are to use an understanding of the meaning of the denominator and numerator to figure out a strategy for finding the solution. 

Type: Lesson Plan

Students will identify the fractional parts of a whole using pattern blocks. There is a focus on unit fractions.

Type: Lesson Plan

Students will make a book of fractions by counting by a specified denominator. They will represent the fractions as pictures, in number form, word form, and on a number line.

Type: Lesson Plan

Students will use paper cutout and geoboards to find and create lines of symmetry. Students will have the opportunity to work with a partner and independently.

Type: Lesson Plan

Students explore how they can compare fractions by considering the denominator. Students use real world examples to create models and demonstrate that the size of the piece decreases as the denominator increases.

Type: Lesson Plan

In this lesson students make number lines out of sentence strips to plot, order, and compare fractions with the same denominators.

Type: Lesson Plan

Students will make and use a set of fraction manipulatives including whole, halves, fourths, and eighths to represent parts of a whole. They may be used later to discover fraction relationships.

Type: Lesson Plan

Students will use foldables to create and name fractions. Students will sing a song to learn the terms numerator and denominator. Students will identify how many unit fractions compose a fraction.

Type: Lesson Plan

The students will use pattern blocks to demonstrate fractions and equivalent fractions. They begin by finding and modeling equivalent fractions with pattern blocks, then they are asked to match cards to show the equivalent fractions.

Type: Lesson Plan

In this lesson, students will demonstrate their understanding of comparing fractions with the same denominator through engaging problem solving. Students will plot fractions on a numberline, play fraction war and complete a worksheet.

Type: Lesson Plan

Students will demonstrate their understanding of comparing fractions with the same numerator through engaging problem solving using real-world application with brownies as a model. Students will be actively engaged in a fraction war game and "would you rather have" statements to solidify their understanding of comparing fractions with the same numerator.

Type: Lesson Plan

In this lesson, students will place fractions on a number line and identify equivalent fractions. Students will explain the definition of equivalent fractions.

Type: Lesson Plan

In this lesson, students will use fold papers to create models to represent equivalent fractions. They will be able to identify representations of equivalence.

Type: Lesson Plan

In this lesson, 3rd grade students will compare fractions which have the same numerator and explain their reasoning. The students will be able to compare the fractions by correctly placing them on a number line.

Type: Lesson Plan

In this lesson, students will build the understanding of unit fractions. They will differentiate examples and non-examples of fractional parts of squares. They will label unit fractions and describe unit fractions as those that “build” other fractions.

Type: Lesson Plan

Students will identify equivalent fractions to 1/2 using manipulatives and determine what happened to the numerator and denominator when an equivalent fraction was formed.  They will practice this idea by identifying equivalent fractions in a domino game.

Type: Lesson Plan

In this lesson, students will use Cuisenaire rods to measure lengths and generate equivalent fractions. This is a concrete way to introduce how to generate equivalent fractions by finding patterns in the numerators and denominators.

Type: Lesson Plan

In this lesson students create a model of a number line using string and adding machine tape. Students discover how to partition the string into equal sections, and name the fractional pieces, including fractions greater than 1.

Type: Lesson Plan

Learn about unit fractions and how to partition number lines to plot unit fractions' locations. Join Nik, Natalia, and their neighborhood friends on a number line fraction finding adventure in this interactive tutorial.

Type: Original Student Tutorial

Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.

Type: Original Student Tutorial

Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.

Type: Original Student Tutorial

Joey learns about the location of unit fractions on a number line while at camp in this interactive tutorial.

Type: Original Student Tutorial

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA). In the optional twist, students will need to modify their original diet for a senior chimpanzee. The first video provided meal planning information to add to the knowledge students gained throughout the unit to start the challenge.

Type: Original Student Tutorial

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout the unit. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food.

In the optional twist, students will need to modify their original diet for a senior chimpanzee. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

Learn to name or identify fractions, especially unit fractions, and justify the fractional value using an area model in this pizza-themed, interactive tutorial.

Type: Original Student Tutorial

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

Type: Original Student Tutorial

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Type: Presentation/Slideshow

This task is designed to help students focus on the whole that a fraction refers. It provides a context where there are two natural ways to view the coins.  While the intent is to deepen a student's understanding of fractions, it does go outside the requirements of the standard. 

Type: Problem-Solving Task

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Type: Problem-Solving Task

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Type: Problem-Solving Task

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Type: Problem-Solving Task

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Type: Problem-Solving Task

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Type: Problem-Solving Task

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Type: Problem-Solving Task

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.

Type: Problem-Solving Task

The purpose of this task is for students to identify which fraction is closest to the whole number 1.

Type: Problem-Solving Task

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Type: Problem-Solving Task

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

Type: Problem-Solving Task

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

Type: Problem-Solving Task

In this activity, students highlight portions of circles or squares that are equivalent to a given fraction. As the student highlights sections, a pointer on a number line between zero and one updates so they can see when they are close or equal to the given fraction. This activity allows students to explore equivalent fractions by making it necessary that each of the three fractions have a different denominator but have the fractions be equal. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Problem-Solving Task

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

By making popcorn together with your child you may also introduce the concept of fractions.

Type: Teaching Idea

In this Khan Academy video four fractions are compared by plotting them on a number line and drawing models.

Type: Tutorial

Use fraction models and a number line to represent 1 as a fraction.

Type: Tutorial

Students will view a video that explains that a fraction is the quantity formed by 1 part when a whole is partitioned into equal parts. Students will then have opportunities to practice this concept with assorted problems and are given immediate feedback as to the accuracy of their responses.

Type: Tutorial

This tutorial for student audiences reviews basic introductory information on fractions. Students will review that a fraction is part of a whole, a fraction is less than 1 whole thing, but more than 0, how to determine pieces of a whole and how to write fractions.

Type: Tutorial

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

• Build equivalent fractions using numbers and pictures.
• Compare fractions using numbers and patterns
• Recognize equivalent simplified and unsimplified fractions

Type: Virtual Manipulative

Match shapes and numbers to earn stars in this fractions game.

• Match fractions using numbers and pictures
• make the same fractions using different numbers
• Match fractions in different picture patterns
• Compare fractions using numbers and patterns

Type: Virtual Manipulative

In this interactive activity users are given pies. Part of the pie is shaded yellow and the total number of pieces is given. The user has to identify the fraction by entering the part divided by the whole. Once the user completes ten problems the score is given.

Type: Virtual Manipulative

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

An interactive tool to represent a fraction circle, rectangle, or set model with numerators and denominators ranging from 1 to 100. The decimal and percent equivalents of the created fraction are also displayed.

Type: Virtual Manipulative